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Q. No.The de-Broglie wavelength of the electron accelerated through a potential difference \(V\) equals the de-Broglie wavelength of an electron in the ground state of the hydrogen atom. The value of \(V\) is:
1. \(13.6\) volts
2. \(27.2\) volts
3. \(10.2\) volts
4. \(6.8\) volts
Subtopic: Â De-broglie Wavelength |
 76%
Level 2: 60%+
Hints
The de-Broglie wavelength of a photon of energy \(E\) is \(\lambda_{ph}\) and that of an electron (non-relativistic) of the same energy \(E\) is \(\lambda_{e}.\) Then (assume \(E\text ~\)few \(e\text{V}\)):
1. \(\lambda_{ph}=\lambda_e\)
2. \(\lambda_{ph}<\lambda_e\)
3. \(\lambda_{ph}>\lambda_e\)
4. any of the above may be true
1. \(\lambda_{ph}=\lambda_e\)
2. \(\lambda_{ph}<\lambda_e\)
3. \(\lambda_{ph}>\lambda_e\)
4. any of the above may be true
Subtopic: Â De-broglie Wavelength |
Level 3: 35%-60%
Hints
A hydrogen atom \((\mathrm{H})\) and a helium \((\mathrm{He})\) atom, both have the same kinetic energy (they are non-relativistic). Their de-Broglie wavelengths are in the ratio: \(\Large\frac{\lambda_\mathrm{H}}{\lambda_{\mathrm{He}}}=\)
| 1. | \(4\) | 2. | \(\dfrac14\) |
| 3. | \(2\) | 4. | \(\dfrac12\) |
Subtopic: Â De-broglie Wavelength |
 74%
Level 2: 60%+
Hints
In an experiment on the photoelectric effect, the maximum kinetic energy of the emitted electrons is plotted as a function of the frequency of incident radiation. The graph is:
| 1. | a straight line with a positive intercept on the \(x\)-axis (frequency) |
| 2. | a straight line with a positive intercept on the \(y\)-axis (kinetic energy) |
| 3. | a parabola |
| 4. | a hyperbola |
Subtopic: Â Photoelectric Effect: Experiment |
 72%
Level 2: 60%+
Hints
Which, of the following, shows the correct graph of the de-Broglie wavelength \((\lambda)\) of a particle and its kinetic energy \((E_K)?\)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Â De-broglie Wavelength |
 78%
Level 2: 60%+
Hints
Select the correct option based on the statements given below:
| Statement I: | By de-Broglie's hypothesis momentum of an electron, \(p=h/ \lambda\). |
| Statement II: | The energy of an electron is given by; \(E=hc/ \lambda\). |
| 1. | Statement I is correct and Statement II is incorrect. |
| 2. | Statement I is incorrect and Statement II is correct. |
| 3. | Both Statement I and Statement II are correct. |
| 4. | Both Statement I and Statement II are incorrect. |
Subtopic: Â De-broglie Wavelength |
 52%
Level 3: 35%-60%
Hints
Photons and electrons of the same wavelength are compared. Which one carries larger momentum?
| 1. | photon |
| 2. | electron |
| 3. | neither, since both have equal momenta |
| 4. | it could be either, depending on the energy |
Subtopic: Â De-broglie Wavelength |
 66%
Level 2: 60%+
Hints
The de-Broglie wavelength of an electron in the ground state of a \(\mathrm H\text -\)atom is \(\lambda_1\) and that on the \(\mathrm{He}^{+}\text -\)ion is \(\lambda_2.\) The kinetic energies of the electrons in the \(\mathrm H\text -\)atom and the \(\mathrm{He}^{+}\text -\)ion-having the same de-Broglie wavelength are \(E_1\) and \(E_2.\) The ratio \(\dfrac{\lambda_1}{\lambda_2}\) is:
| 1. | \(4\) | 2. | \(2\) |
| 3. | \(\dfrac12\) | 4. | \(\dfrac14\) |
Subtopic: Â De-broglie Wavelength |
 56%
Level 3: 35%-60%
Hints
Light of wavelength \(4000~\mathring{A}\) is incident on a metal whose work function is \(2.0\) eV. The fastest photo-electrons emitted have an energy of:
(Take \(hc=12400\) eV-\(\mathring A\))
1. \(0.5\) eV
2. \(3.1\) eV
3. \(1.1\) eV
4. \(2\) eV
(Take \(hc=12400\) eV-\(\mathring A\))
1. \(0.5\) eV
2. \(3.1\) eV
3. \(1.1\) eV
4. \(2\) eV
Subtopic: Â Einstein's Photoelectric Equation |
 82%
Level 1: 80%+
Hints
Ultraviolet photons, each of energy \(20~\text{eV},\) are incident onto a gas of \(\mathrm {H}\)-atoms, causing the emission of electrons. The kinetic energy of the emitted electrons has the value:
1. \(6.4~\text{eV}\)
2. \(7.2~\text{eV}\)
3. \(3.2~\text{eV}\)
4. \(13.6~\text{eV}\)
1. \(6.4~\text{eV}\)
2. \(7.2~\text{eV}\)
3. \(3.2~\text{eV}\)
4. \(13.6~\text{eV}\)
Subtopic: Â Electron Emission |
 68%
Level 2: 60%+
Hints
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